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Bosonization
In theoretical condensed matter physics, Bosonization is a mathematical procedure by which a system of interacting fermions in (1+1) dimensions can be transformed to a system of massless, non-interacting bosons.[1] The method of bosonization was conceived independently by particle physicists Sidney Coleman and Stanley Mandelstam; and condensed matter physicists Daniel Mattis and Alan Luther in 1975.[1]
The basic physical idea behind bosonization is that particle-hole excitations are bosonic in character. However, it was shown by Tomonaga in 1950 that this principle is only valid in one-dimensional systems.[2] Bosonization is an effective field theory that focuses on low-energy excitations.[3] This is done for Luttinger liquid theory.
Two complex fermions \psi,\bar\psi are written as functions of a boson \(\phi \)
\( \bar\psi_-\psi_+ = :\exp(i\phi):,\qquad \bar\psi_-\psi_+ = :\exp(-i\phi) \):[4]
while the inverse map is given by
\( \partial\phi=:\bar\psi\psi: \)
All equations are normal-ordered. The changed statistics arises from anomalous dimensions of the fields.
See Also
Luttinger Liquid
References
Gogolin, Alexander O. (2004). Bosonization and Strongly Correlated Systems. Cambridge University Press. ISBN 0-521-61719-7.
Sénéchal, David (1999). "An Introduction to Bosonization". Theoretical Methods for Strongly Correlated Electrons. CRM Series in Mathematical Physics. doi:10.1007/0-387-21717-7_4.
Sohn, Lydia (ed.) (1997). Mesoscopic electron transport. Springer. arXiv:cond-mat/9610037. ISBN 0-7923-4737-4.
In actuality, there is a cocycle prefactor to give correct (anti-)commutation relations with other fields under consideration.
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